Lecture 6 Newtons Third Law Newtons 3 rd

Lecture 6: Newton’s Third Law • Newton’s 3 rd Law • Action-reaction pairs • Inclined coordinate system • Massless ropes and massless, frictionless pulleys • Coupled objects

Newton’s 3 rd Law Common version: For every action there is an equal and opposite reaction. * *This is problematic because it suggests that first there is an action and then there is a reaction. Better version:

Action-reaction pairs

Example: object at rest on a table Forces of action-reaction pair act on two different objects

Object on inclined plane Normal = perpendicular Normal force must be perpendicular to surface Weight: vertically down

Object on inclined plane Choose axis in direction of acceleration. Draw components of weight vector Identify θ in the weight triangle

Components of weight vector In this coordinate system:

Coupled objects: ropes and pulleys We make the following approximations: • massless, un-stretchable rope → tension is constant throughout the rope • massless, frictionless pulley → tension remains constant as rope passes over pulley Caution: If mass and spatial extension of the pulley are taken into account, the tension does not remain constant! We will study this with Rotational Motion in lectures 18 -21.

Example with coupled objects Two blocks are connected by a massless string. A block of mass m is on a frictionless inclined plane that makes angle θ with the vertical, while a block of mass M hangs over a massless and frictionless pulley. Derive an expression for the acceleration of the blocks in terms of relevant system parameters.